Amortized Localized Posterior Inference for Model Calibration with Application to an Ocean Turbulence Closure

# Amortized Localized Posterior Inference for Model Calibration with Application to an Ocean Turbulence Closure
Source: [https://arxiv.org/abs/2610.37731](https://arxiv.org/abs/2610.37731)
[View PDF](https://arxiv.org/pdf/2610.37731)

> Abstract:Model discrepancy may prevent a single calibration parameter from reproducing a physical response across the context domain\. In addition, uncertainties in observations and contexts affect calibration and must be accounted for and quantified\. We construct a family of localized posteriors by weighting observation likelihoods according to their proximity to a target context\. Gaussian localization weights incorporate context uncertainty through covariance inflation, with reflection at domain boundaries and an optional correction for uneven context sampling\. A conditional normalizing flow approximates the family of posteriors through amortized variational inference\. Integrating the localized posteriors under a prescribed context measure gives the marginalized parameter distribution\. In a twin experiment with the Branin\-Hoo model, we compare global and localized inference under uniform and skewed context distributions\. Localization reduces the reported aggregate predictive errors relative to the global posterior\. An application to the k\-$\\epsilon$ turbulence closure in a single\-column ocean model, with atmospheric surface forcing as context, shows that localized posterior calibration reduces temperature and zonal\-velocity errors relative to deterministic and global\-posterior calibration\. Both twin experiments are constructed to admit local compensation\.

## Submission history

From: Exauce LUWEH ADJIM NGARTI \[[view email](https://arxiv.org/show-email/ec12bbeb/2610.37731)\] \[via CCSD proxy\] **\[v1\]**Tue, 27 Oct 2026 12:50:10 UTC \(3,312 KB\)